State-space modeling of the relationship between air quality and mortality

A portion of a population is assumed to be at risk, with the mortality haza rd varying with atmospheric conditions including total suspended particulat es (TSP). This at-risk population is not observed and the hazard function i s unknown; we wish to estimate these from mortality count and atmospheric v ariables. Consideration of population dynamics leads to a state-space repre sentation, allowing the Kalman Filter (KF) to be used for estimation. A har vesting effect is thus implied; high mortality is followed by lower mortali ty until the population is replenished by new arrivals. The model is applied to daily data for Philadelphia, PA, 1973-1990. The est imated hazard function rises with the level of TSP and at extremes of tempe rature and also reflects a positive interaction between TSP and temperature . The estimated at-risk population averages about 480 and varies seasonally . We find that lags of TSP are statistically significant, but the presence of negative coefficients suggests their role may be partially statistical r ather than biological. In the population dynamics framework, the natural me tric for health damage from air pollution is its impact on life expectancy. The range of hazard rates over the sample period is 0.07 to 0.085, corresp onding to life expectancies of 14.3 and 11.8 days, respectively.